Question

A jungle veterinarian with a blow-gun loaded with a tranquilizer dart and a sly 1.5 kg monkey are each a height 27 meters above the ground in trees a distance 98 meters apart. Just as the hunter shoots horizontally at the monkey, the monkey drops from the tree in a vain attempt to escape being hit.What must the minimum muzzle velocity of the dart have been for the hunter to hit the monkey before it reached the ground?v= ? m/s

Answer 1

Since monkey is dropped from the tree as soon as He shoot the dart on it

so here the time taken by the monkey to reach the ground is given by kinematics

so it is given as

`y = (1)/(2)gt^2`

given that

y = 27 m

now we have

`27 = (1)/(2)(9.8)t^2`

`t = 2.35 s`

now the dart should reach the monkey in same time

so the horizontal distance between dart and monkey is given as

`x = 98 m`

time = 2.35 s

speed = distance / time

now from above equation we have

`v = (98)/(2.35)`

`v = 41.75 m/s`